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Sets whose intersection is the empty set are called disjoint. What is the opposite of a disjoint set? For example the sets $\{1,2\}$ and $\{2,3\}$ satisfy this condition. I know that you can just say not-disjoint. But I was wondering if there was a specific term for it. I ask this because someone told me that this term existed but that he could`nt remeber. I have searched extensively but I haven't found it.

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5  
I always say two sets "intersect" or that they "have nonempty intersection". –  Alex Becker Jul 10 '12 at 1:51
6  
"Non-disjoint". –  MJD Jul 10 '12 at 1:52
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They are joint! –  William Jul 10 '12 at 1:53

2 Answers 2

up vote 6 down vote accepted

If $A\cap B \not= \emptyset$, I say, "$A$ meets $B$."

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I don't just say this, Erdos does: renyi.hu/~p_erdos/1955-14.pdf (Proof of Theorem 2). Pontryagin also uses the term in his topology book. I learned the term from topologists at the University of Texas back in the 80s. It is a descriptive and useful one. I do not understand the downvote. –  ncmathsadist Jul 10 '12 at 22:24
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@Norbert: seriously? –  Asaf Karagila Jul 16 '12 at 13:50
    
@Asaf Karagila, Seriously. –  no identity Jul 16 '12 at 13:50

You seem to be looking for an adjective meaning the opposite of disjoint. Given two sets that aren't disjoint, I would just call them intersecting sets, where intersecting is an adjectival participle derived from the verb to intersect.

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